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-rw-r--r--graphics/pstricks/contrib/pst-func/doc/pst-func-doc.bib8
-rw-r--r--graphics/pstricks/contrib/pst-func/doc/pst-func-doc.pdfbin4050523 -> 4065407 bytes
-rw-r--r--graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex107
3 files changed, 102 insertions, 13 deletions
diff --git a/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.bib b/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.bib
index e749f71bfb..89f7eaad31 100644
--- a/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.bib
+++ b/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.bib
@@ -166,3 +166,11 @@
year = {2012},
url = {/graphics/pstricks/contrib/pst-tools}
}
+
+@online{weisstein,
+ author = {Weisstein, Eric W.},
+ title = {Noncentral Student's t-Distribution},
+ subtitle = {From MathWorld--A Wolfram Web Resource},
+ url = {https://mathworld.wolfram.com/NoncentralStudentst-Distribution.html},
+ note = {Probability and Statistics; Statistical Distributions; Continuous Distributions }
+ }
diff --git a/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.pdf b/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.pdf
index b791d5e480..62249b7e51 100644
--- a/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.pdf
+++ b/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.pdf
Binary files differ
diff --git a/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex b/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex
index 8e87d3a6d3..b3f0c2ecae 100644
--- a/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex
+++ b/graphics/pstricks/contrib/pst-func/doc/pst-func-doc.tex
@@ -1,6 +1,6 @@
\RequirePackage{pdfmanagement-testphase}
\DeclareDocumentMetadata{}
-%% $Id: pst-func-doc.tex 306 2021-10-29 14:48:08Z herbert $
+%% $Id: pst-func-doc.tex 691 2023-04-03 10:51:04Z herbert $
\documentclass[fontsize=11pt,english,BCOR=10mm,DIV=12,bibliography=totoc,parskip=false,headings=small,
headinclude=false,footinclude=false,oneside]{pst-doc}
\usepackage{pst-func}
@@ -1158,7 +1158,7 @@ f(t) = constI \cdot J_n + constII
where \Lkeyword{constI} and \Lkeyword{constII} must be real PostScript expressions, e.g.
\begin{lstlisting}[style=syntax]
-\psset{constI=2.3,constII=t k sin 1.2 mul 0.37 add}
+\psset{constI=2.3,constII=t toDegrees sin 1.2 mul 0.37 add}
\end{lstlisting}
The Bessel function is plotted with the parametricplot macro, this is the
@@ -1174,13 +1174,11 @@ In particular, note that the default for
time consuming at this setting, it can be decreased in the usual
way, at the cost of some reduction in graphics resolution.
-\begin{LTXexample}
-{
+\begin{LTXexample}[pos=t]
\psset{xunit=0.25,yunit=5}
\begin{pspicture}(-13,-.85)(13,1.25)
\rput(13,0.8){%
- $\displaystyle J_n(x)=\frac{1}{\pi}\int_0^\pi\cos(x\sin t-nt)\dt$%
-}
+ $\displaystyle J_n(x)=\frac{1}{\pi}\int_0^\pi\cos(x\sin t-nt)\dt$}
\psaxes[Dy=0.2,Dx=4]{->}(0,0)(-30,-.8)(30,1.2)
\psset{linewidth=1pt}
\psBessel[linecolor=red]{0}{-28}{28}%
@@ -1188,23 +1186,21 @@ way, at the cost of some reduction in graphics resolution.
\psBessel[linecolor=green]{2}{-28}{28}%
\psBessel[linecolor=magenta]{3}{-28}{28}%
\end{pspicture}
-}
\end{LTXexample}
-\begin{LTXexample}
-{
+
+\begin{LTXexample}[pos=t]
\psset{xunit=0.25,yunit=2.5}
\begin{pspicture}(-13,-1.5)(13,3)
\rput(13,0.8){%
- $\displaystyle f(t) = 2.3 \cdot J_0 + 1.2\cdot \sin t + 0.37$%
-}
+ $\displaystyle f(t) = 2.3 \cdot J_0 + 1.2\cdot \sin t + 0.37$}
\psaxes[Dy=0.8,dy=2cm,Dx=4]{->}(0,0)(-30,-1.5)(30,3)
\psset{linewidth=1pt}
-\psBessel[linecolor=red,constI=2.3,constII={t k sin 1.2 mul 0.37 add}]{0}{-28}{28}%
+\psBessel[linecolor=red,constI=2.3,constII={t toDegrees sin 1.2 mul 0.37 add}]{0}{-28}{28}%
\end{pspicture}
-}
\end{LTXexample}
+
%\clearpage
\subsection{Modfied Bessel function of first order}
The modified Bessel function of first order is defined as
@@ -1216,6 +1212,7 @@ I_\nu(x) &= \left(\frac12 x\right)^\nu
%
\noindent The syntax of the macro is
+
\begin{BDef}
\Lcs{psModBessel}\OptArgs\Largb{xStart}\Largb{xEnd}
\end{BDef}
@@ -1223,6 +1220,11 @@ I_\nu(x) &= \left(\frac12 x\right)^\nu
The only valid optional argument for the function is \Lkeyword{nue}, which
is preset to 0, it shows $I_0$.
+
+
+
+
+
\begin{LTXexample}
\begin{pspicture}(0,-0.5)(5,5)
\psaxes[ticksize=-5pt 0]{->}(5,5)
@@ -1909,6 +1911,70 @@ and the following syntax
%The $t_\nu$-distribution has mode 0.
+\subsection{Student's noncentral $t$-distribution}
+
+
+A generalization of Student's t-distribution known as the noncentral Student's t-distribution is given by
+
+\[
+ P(x)=\frac{\nu^{\nu/2}\nu!}{2^{\nu}e^{\lambda^2/2}(\nu+x^2)^{\nu/2}\Gamma(\frac12\nu)}
+ \left\{
+ \frac{\sqrt{2}\lambda x\, {}_1F_1\left(\frac12 \nu+1;\, \frac32; \,\frac{\lambda^2x^2}{2(\nu+x^2)}\right)}
+ {(\nu+x^2)\Gamma[\frac12(\nu+1)]}
+ + \frac{{}_1F_1\left(\frac12(\nu+1);\, \frac12; \, \frac{\lambda^2x^2}{2(\nu+x^2)}\right)}{\sqrt{\nu+x^2}\Gamma(\frac12\nu+1)}\right\}
+\]
+
+where $\Gamma(z)$ is the gamma function and ${}_1F_1(a;b;z)$ is a confluent hypergeometric function of the first kind.~\parencite{weisstein}
+
+
+\[ {}_1F_1(a;b;z) = 1+\frac ab z + \frac{a(a+1)}{b(b+1)} \frac{z^2}{2!}+ \cdots=\sum_{k=0}^\infty\frac{(a)_k}{(b)_k} \frac{z^k}{k!} \]
+
+
+%mu = lambdasqrt(n/2)(Gamma(1/2(n-1)))/(Gamma(1/2n))
+%sigma^2 = ((lambda^2+1)n)/(n-2)-(lambda^2n[Gamma(1/2(n-1))]^2)/(2[Gamma(1/2n)]^2).
+
+The macro has the same syntax as the centered Student's distribution:
+
+\begin{BDef}
+\Lcs{psNonCentralTDist}\OptArgs\Largb{x0}\Largb{x1}
+\end{BDef}
+
+
+There exists an additional optional parameter \Lkeyword{lambda}, which is preset to 0.5.
+
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{xunit=0.75cm,yunit=10cm}
+\begin{pspicture}(-6,-0.1)(11,.5)
+ \psaxes[Dy=0.1]{->}(0,0)(-4.5,0)(10,0.5)
+ \psset{linewidth=1pt,plotpoints=100}
+ \psNonCentralTDist[linecolor=red,lambda=0,nue=1]{-5}{10}% same as \psTDist
+ \psNonCentralTDist[linecolor=green,lambda=0,nue=4]{-5}{10}% dito
+ \psNonCentralTDist[linecolor=red,lambda=2,nue=1]{-5}{10}
+ \psNonCentralTDist[linecolor=green,lambda=2,nue=4]{-5}{10}
+\end{pspicture}
+\end{LTXexample}
+
+
+
+
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{xunit=1.25cm,yunit=10cm}
+\begin{pspicture}(-6,-0.1)(6,.5)
+ \psaxes[Dy=0.1]{->}(0,0)(-4.5,0)(5.5,0.5)
+ \psset{linewidth=1pt,plotpoints=100}
+ \psTDist[linecolor=blue]{-4}{4}
+ \psNonCentralTDist[linecolor=red]{-4}{5}
+ \psNonCentralTDist[linecolor=green,nue=4,lambda=2]{-4}{5}
+\end{pspicture}
+\end{LTXexample}
+
+
+
+
+
+
\clearpage
\subsection{$F$-distribution}
A continuous statistical distribution which arises in the testing of
@@ -2173,6 +2239,21 @@ origin of the coordinate system.
\endpsgraph
\end{LTXexample}
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{lly=-13mm,llx=-5mm}
+\psgraph[Dx=0.2,Dy=0.2,axesstyle=frame](0,0)(1,1){6cm}{6cm}
+\psline[linestyle=dashed](1,1)
+\psLorenz[Gini,linecolor=red,linewidth=1.5pt]<.2 .2 .2 .2 .2>{.1 .1 .1 .35 .35 }
+\psLorenz[Gini,linecolor=blue,linestyle=dashed,linewidth=1.5pt]{.1 .1 .1 .35 .35 }
+\endpsgraph
+\end{LTXexample}
+
+
+
+
+
+
\clearpage
\subsection{\nxLcs{psLame} -- Lam\'e Curve, a superellipse}
A superellipse is a curve with Cartesian equation